Challenges for forecasting based on accelerating rates of earthquakes at volcanoes and laboratory analogues

P>'Mean-field' models have been proposed as falsifiable hypotheses for the acceleration in earthquake rate and other geophysical parameters prior to laboratory rock failure and volcanic eruptions. Importantly, such models may permit forecasting failure or eruption time. However, in existing retrospective analyses it is common to find examples of inappropriate techniques for fitting these models to data. Here we test the two main competing hypotheses-exponential and power-law acceleration-using maximum likelihood techniques and an information criterion for model choice, based on a Poisson process with variable rate. For examples from the laboratory and Mt Etna, the power law is clearly the best model, both in terms of the fit and the resulting error structure, which is consistent with the Poisson approximation. For examples from Kilauea and Mauna Loa the results are less clear-cut and the confidence interval underestimates the number of outliers. Deviations from the models most likely reflect local interactions and/or non-stationary loading processes not captured by the mean-field approach. In addition, we use simulations to demonstrate an inherent problem with model preference, in that a power-law model will only be preferred if failure or eruption occurs close to the singularity. Although mean-field models may well provide valuable insight into the physical process responsible for precursory accelerations in earthquake rate, our findings highlight major difficulties that must be overcome to use such models for forecasting.